1. Field of the Invention
The present invention relates to a method for data communication of signals in units of a frame using an orthogonal frequency division modulation (OFDM) algorithm, and in particular, to methods of estimating carrier frequency offset error at the receiver.
2. Description of the Prior Art
OFDM system is a viable modulation scheme for data transmission time varying dynamic channels. However, it is known that performance of such system is highly susceptible to non-ideal synchronization parameters. Specifically, symbol timing and carrier frequency offset become an increasingly important issue in implementation of OFDM systems for practical applications. It is known that carrier frequency offset deteriorates performance of OFDM systems by introducing interference among the sub-channels. To overcome this imperfection, various compensation methods for estimation and correction of synchronization parameters have been proposed. In order to compare the performance of these estimators, it is required to define a single number representing the goodness of the estimate. Assuming that all estimators are unbiased, i.e., expectation of the estimate is equal to the parameter, the variance of the estimator is used as a global measure for performance comparison of these estimators.
Cramer-Rao lower bound (CRLB) is a fundamental lower bound on the variance of the estimators and the unbiased estimator whose variance equals CRLB is called efficient. When the evaluation of efficient estimator is not possible, it is desirable to obtain an estimator in which its performance becomes as close as possible to the CRLB fundamental bound. The estimator which is closest in performance to the CRLB estimator is known as a minimum variance unbiased (MVU) estimator.
Categorically, the previously proposed methods for synchronization of OFDM systems can be classified into two main subclasses, namely minimum mean square error (MMSE) and maximum likelihood (ML) estimators. In MMSE approach, the estimator uses the information provided by the reference signal (pilot tones) in order to minimize a cost function associated with the synchronization parameters. A salient feature of this approach is that no probabilistic assumptions are made with regard to the data. Although MMSE estimators usually result in a tractable (globally stable) and easy to implement realization, no optimal criteria (probabilistic) is associated with these estimators. Also, since part of the transmitted information is allocated to the reference pilots, the bandwidth efficiency of these methods is lower in comparison to the non-pilot schemes.
On the other hand, ML estimators provide the estimate of the unknown parameter subject to minimum probability of error criteria. Although not exactly efficient, ML estimators are asymptotically MVU, i.e., their variance attains that of MVU estimator as the length of data record goes to infinity. However, due to the physical constraints, systems with infinitely long data records are not feasible for implementation purposes.
P. H. Moose, in “A Technique for Orthogonal Frequency Division Multiplexing Frequency Offset Correction,” in IEEE Trans. On Communications, Vol. 42, No. 10, pp. 2908–2913, October 1994, describes the use of a retransmission technique in order to reveal the frequency offset parameter in the likelihood function of the received signal. Due to the redundancy introduced by repeating the data block, the data rate efficiency is decreased by a factor of two. To avoid this imperfection, a ML estimator based on cyclic prefix (CP) is described by J. van de Beck, M. Sandel and P. O. Borjesson, in “ML Estimation of Timing and Frequency Offset in OFDM Systems,” IEEE Trans. On Signal Processing, Vol. 45, No. 3, pp. 1800–1805, July 1997. In this approach, the side information provided by the CP is used to obtain the likelihood function for joint estimation of symbol timing error and frequency offset in an OFDM system.
The likelihood function described in the Moose reference does not globally characterize the observation vector over the entire range of the timing offset. Consequently, the ML estimator proposed based on this likelihood function would result in considerable performance loss over a finite range of timing offset interval.
Currently, there is increasing interest in multi-carrier modulation (MCM) for dividing a communication channel into several subchannels and transmitting many subcarriers through a single band using frequency division multiplexing (FDM) techniques. In the MCM method, however, because several subcarriers occupying a narrow frequency domain are transmitted at one time, a relatively longer symbol period results compared with a single carrier modulation method. The MCM method has, owing to such characteristics, the advantages that equalization is easily performed and that it has immunity to impulse noise. OFDM is a type of the MCM designed to maximize the working frequency efficiency by securing orthogonality among the multiplexed subcarriers. OFDM is applied to mobile radio channels to attenuate multipath fading.
In an OFDM transmitting/receiving system, modulation and demodulation of parallel data are carried out using the Fast Fourier Transform (FFT). It is required that the sampled data be sent in predetermined frames, having passed through a FFT routine, been time-division multiplexed, and transmitted, then restored at the receiving end. However, if the synchronization is in error in the course of restoring the frame, the signals demodulated after the FFT will be influenced by interchannel and intersymbol interference. Accordingly, the problem of synchronization in reforming the frame, especially any joint carrier frequency offset or symbol timing error, must be addressed as a matter of importance.
Conventional synchronization methods as above-described encounter problems in that the process of synchronization is not only very complex, but the synchronization is not realized rapidly.